(2t-5)(6t+1)=(4t-3)(3t+6)

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Solution for (2t-5)(6t+1)=(4t-3)(3t+6) equation: 


Simplifying
(2t + -5)(6t + 1) = (4t + -3)(3t + 6)

Reorder the terms:
(-5 + 2t)(6t + 1) = (4t + -3)(3t + 6)

Reorder the terms:
(-5 + 2t)(1 + 6t) = (4t + -3)(3t + 6)

Multiply (-5 + 2t) * (1 + 6t)
(-5(1 + 6t) + 2t * (1 + 6t)) = (4t + -3)(3t + 6)
((1 * -5 + 6t * -5) + 2t * (1 + 6t)) = (4t + -3)(3t + 6)
((-5 + -30t) + 2t * (1 + 6t)) = (4t + -3)(3t + 6)
(-5 + -30t + (1 * 2t + 6t * 2t)) = (4t + -3)(3t + 6)
(-5 + -30t + (2t + 12t2)) = (4t + -3)(3t + 6)

Combine like terms: -30t + 2t = -28t
(-5 + -28t + 12t2) = (4t + -3)(3t + 6)

Reorder the terms:
-5 + -28t + 12t2 = (-3 + 4t)(3t + 6)

Reorder the terms:
-5 + -28t + 12t2 = (-3 + 4t)(6 + 3t)

Multiply (-3 + 4t) * (6 + 3t)
-5 + -28t + 12t2 = (-3(6 + 3t) + 4t * (6 + 3t))
-5 + -28t + 12t2 = ((6 * -3 + 3t * -3) + 4t * (6 + 3t))
-5 + -28t + 12t2 = ((-18 + -9t) + 4t * (6 + 3t))
-5 + -28t + 12t2 = (-18 + -9t + (6 * 4t + 3t * 4t))
-5 + -28t + 12t2 = (-18 + -9t + (24t + 12t2))

Combine like terms: -9t + 24t = 15t
-5 + -28t + 12t2 = (-18 + 15t + 12t2)

Add '-12t2' to each side of the equation.
-5 + -28t + 12t2 + -12t2 = -18 + 15t + 12t2 + -12t2

Combine like terms: 12t2 + -12t2 = 0
-5 + -28t + 0 = -18 + 15t + 12t2 + -12t2
-5 + -28t = -18 + 15t + 12t2 + -12t2

Combine like terms: 12t2 + -12t2 = 0
-5 + -28t = -18 + 15t + 0
-5 + -28t = -18 + 15t

Solving
-5 + -28t = -18 + 15t

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-15t' to each side of the equation.
-5 + -28t + -15t = -18 + 15t + -15t

Combine like terms: -28t + -15t = -43t
-5 + -43t = -18 + 15t + -15t

Combine like terms: 15t + -15t = 0
-5 + -43t = -18 + 0
-5 + -43t = -18

Add '5' to each side of the equation.
-5 + 5 + -43t = -18 + 5

Combine like terms: -5 + 5 = 0
0 + -43t = -18 + 5
-43t = -18 + 5

Combine like terms: -18 + 5 = -13
-43t = -13

Divide each side by '-43'.
t = 0.3023255814

Simplifying
t = 0.3023255814

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